The Proxy-SU(3) Symmetry in Atomic Nuclei

Abstract

The microscopic origins and the current predictions of the proxy-SU(3) symmetry model of atomic nuclei were reviewed. Beginning with experimental evidence for the special roles played by nucleon pairs with maximal spatial overlap, the proxy-SU(3) approximation scheme is introduced; its validity is demonstrated through Nilsson model calculations and its connection to the spherical shell model. The major role played by the highest weight-irreducible representations of SU(3) in shaping up the nuclear properties is pointed out, resulting in parameter-free predictions of the collective variables β and γ for even–even nuclei in the explanation of the dominance of prolate over oblate shapes in the ground states of even–even nuclei, in the prediction of a shape/phase transition from prolate to oblate shapes below closed shells, and in the prediction of specific islands on the nuclear chart in which shape coexistence is confined. Further developments within the proxy-SU(3) scheme are outlined.

Prolate-oblate shape transitions and O(6) symmetry in even–even nuclei: a theoretical overview

“…Shape coexistence (SC) [77,[160][161][162]235] in even-even nuclei refers to the situation in which the ground state band and another K = 0 band lie close in energy but possess radically different structures, for example one of them being spherical and the other one deformed, or both of them being deformed, but one of them having a prolate shape and the other one exhibiting an oblate shape. A dual shell mechanism [202,236] proposed within the proxy-SU(3) scheme [59][60][61] suggests that SC can occur only within certain stripes of the nuclear chart, forming islands of SC, for the borders of which empirical rules have been recently suggested [201]. It is interesting to see where the lines along which a prolate to oblate transition is expected are lying in relation to the islands of SC, depicted in figure 1 of [77].…”

“…Another approximation scheme allowing the use of the SU(3) symmetry in medium mass and heavy nuclei beyond the sd shell, in which the microscopic Elliott SU(3)symmetry [50][51][52][53] is destroyed by the spin-orbit interaction, is the proxy-SU(3) symmetry, introduced by Bonatsos et al in 2017 [59][60][61]191]. The connection of the proxy-SU(3) symmetry to the shell model has been clarified in [192] (see table 7 of [192]), while its connection to the Nilsson model has been demonstrated in [59,193].…”

“…Another alternative path is provided by taking advantage of group theory, since the importance of symmetries in nuclear structure has been recognized by Wigner already in 1937 [49]. A bridge between the shell model and the collective model has been provided in 1958 by the SU(3) model of Elliott [50][51][52][53], on which the pseudo-SU(3) [54][55][56], quasi-SU(3) [57,58], and proxy-SU(3) [59][60][61] models have been later built. The microscopic symplectic model [62,63], as well as its recent extension, the symmetry-adapted no-core-shell model [64][65][66], also make wide use of the SU(3) symmetry techniques [67].…”

Prolate-oblate asymmetric shape phase transition in the interacting boson model with SU (3) higher-order interactions

“…[71][72][73] and the detailed discussions in these papers). In addition, the prolte-oblate shape phase transition was also discussed in the proxy-SU (3) model, which highlights the prolate dominance [74,75]. Recently, an important progress was made that microscopic mechanism based on the shell model is revealed for the oblateprolate shape transition in the Te-Xe-Ba region [76], in which the quadrupole moment is regarded as an important order parameter for the prolate-oblate shape phase transition, and quasi-SU (3) couplings play a critical role in driving shape evolution and phase transition [77,78].…”

Signatures for shape coexistence and shape/phase transitions in even–even nuclei

“…While the initial expectation was that SC can occur anywhere across the nuclear chart, already in 2011, in figure 8 of the authoritative review of [3], it has been observed that nuclei exhibiting experimental signs of SC appear to cluster together into certain islands on the nuclear chart. A possible theoretical justification of the origin of these islands has been given recently in the framework of the proxy-SU(3) symmetry [6][7][8], which restores the SU(3) symmetry of the 3-dimensional isotropic harmonic oscillator (3D-HO) in the nuclear shells beyond the sd shell through replacement of the intruder orbitals by their 'proxies' (which have escaped to the shell below because of the action of the spin-orbit interaction), based on the similarities of the Nilsson quantum numbers characterizing the two sets of orbitals (see the recent review [9] for further details). Within this framework, a dual shell mechanism, based on the interplay of the magic numbers of the 3D-HO and the familiar nuclear magic numbers created by the spin-orbit interaction, has been suggested in 2021 [5].…”